RIESGO FINANCIERO

Appendix I describes the details of each step that the ADOPT model takes to simulate individual prescription behavior. Unlike the methods sections described in other studies, no table of input values is given because the number of input parameters used by the ADOPT model is so huge (>8,000) that it is impossible to show every single value in this report. However, it cannot be expected that a micro-simulation model would effectively represent the diversity of individual prescription behaviors using a handful of input parameters. To account for the diversity, most of this model’s input tables are very specific. For example, there are 126 tables used for a single step of simulating the frequency of the appearance of drug types in an episode of opioid use, each containing 12 columns and up to 21 rows and corresponding to a specific combination of predominant drug type and episode length type. Such detailed specification ensures that the ADOPT mimics the real prescription behavior as closely as possible. Although this report does not have the capacity to list all input parameters, all input values used by the ADOPT can be found in the model (i.e., the Excel file) itself.

Step 1: Simulate the Basic Individual Profile

Creating the prescription history of a hypothetical opioid user begins with creating the basic individual profile. The user defines the population age, gender, and racial/ethnic distribution and the prevalence of risk factors (including depression diagnosis, history of alcohol abuse, and concurrent sedative/hypnotic drug use). To facilitate our following discussion, we will focus on a hypothetical opioid user, “Jane,” who is a 41-year old, white female, with diagnosed depression, no history of alcohol abuse, and concurrent sedative/hypnotic drug use.

Step 2: Simulate Predominant Drug Type in An Episode of Drug Use

This step involves predicting what kind(s) of drugs Jane uses, which can be difficult since Jane can use different types of prescription opioids, either concurrently or successively. Instead of predicting every single opioid that she uses, the ADOPT model first predicts the predominant drug type that she uses for the initial episode of drug use. An episode of drug use is defined as the dispensing date of an opioid prescription with no previous prescription or with a gap longer than 31 days from the run-out date of previous prescription. Episode duration is defined as the number of days from the date of first fill to the run-out date of the last opioid prescription, without any lapses longer than 31 days after the previous refill. The predominant drug type is defined as the most frequently prescribed drug type within an episode.

Predicting the most frequently used opioids (“predominant drug types”) in an episode is achieved through a multinomial logistic regression model. The predictor variables are age stratum

(including 12-17, 18-29, 30-44, and 45-64), gender (male and female), and race (white and non- white) and the predicted variable is the predominant drug type. This model is based on analyses of the MarketScan® data as described in Part 2 of the report. The logic behind the model is that the specific opioid prescription type is associated with these demographic characteristics; therefore, we can use the demographic characteristics to predict, indirectly, the type of opioids used.

The predominant drug types in the MarketScan® data include: hydrocodone, oxycodone, propoxyphene, and tramadol. Each of these four drugs accounts for >10% of the distribution of the most commonly used opioids. Other Schedule II long-acting, other Schedule II short-acting,

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and other non-Schedule II opioids are less commonly used and, therefore, grouped into the latter 3 categories, in order to ensure that the regression model has sufficient predictive power. If an individual falls into any of the latter three categories, a further sampling process based on the age-, gender-, and race-specific distribution of drug types in that category will be done to predict the specific drug used. The drug types under the latter three categories are shown in Table 3-15 below.

Table 3-15. Most Frequently Used Opioid Types in Market Scan Data

Predominant Opioid Types

Less Common Opioid Types Other Schedule II

Long Acting

Other Schedule II

Short Acting Other Non-Schedule II

Hydrocodone +

aspirin/acetaminophen/ibupro

fen Fentanyl transdermal

Hydromorphone Butalbital + codeine (with or without aspirin/acetaminophen/ ibuprofen)

Oxycodone (with or without aspirin/acetaminophen/ibupro fen) Morphine sulfate sustained release Meperidine hydrochloride Butorphanol Propoxyphene (with or without aspirin/acetaminophen/ibupro fen) Oxycodone HCL control release

Morphine sulfate Pentazocine (with or without

aspirin/acetaminophen/ ibuprofen)

Tramadol with or without aspirin

Methadone Codeine Sulfate Codeine +

aspirin/acetaminophen/ ibuprofen Oxymorphone extended release Levorphanol Opium Dihydrocodeine Fentanyl citrate transmucosal Tapentadol

The multinomial logistic regression model gives the predictive value (in percentage) for each category of commonly used opioid types for all possible combinations of the explanatory variables. In the model, the predictive values are translated into cumulative probabilities, as shown in Figure 3-5. The model then generates a random number between 0 and 1 and this number is compared with the cumulative probabilities to decide which interval (i.e., category of predominant drug type) the random number falls in. As shown in Figure 3-5, a row of cumulative probabilities is located for Jane’s age, gender and race. The randomly generated number is 0.72, which is greater than 0.68 (the upper bound for the category of “other Schedule II short-acting”) and smaller than 0.82 (the upper bound for the category of “oxycodone”); therefore, the

predominant drug type for Jane’s initial episode is oxycodone. The output of this simulation process reflects the MarketScan®distribution of predominant drug types.

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Figure 3-5. Example of Random Sampling of Predominant Drug Type

30-44 female white 54% 59% 62% 68% 82% 87% 100% 30-44 male non-white 51% 53% 59% 62% 77% 85% 100% 30-44 male white 55% 58% 62% 66% 78% 86% 100% 45-64 female non-white 46% 49% 54% 58% 74% 82% 100% Age strata

gender race Hydroco done Other_L A_II Other_ Non_II Other_ SA_II Oxycodo ne Propoxy phene Tramado l Generated _random number 0.72 0.72>0.68 and <0.82 Oxycodone

A similar technique is used repeatedly in the following steps. No detailed description is provided again.

Step 3: Simulate Episode Length

Predicting episode length is achieved through another multinomial logistic regression model based on the MarketScan®database. The predictor variables are age, gender, race and the

predominant drug type sampled in Step 2. The logic behind this regression model is that drug use duration is related to both demographic characteristics (which are associated with pain

type/severity and likelihood of drug abuse) and the drug type(s) used. The predicted variable is the episode length, categorized into 0-29 days (short term), 30-59 days, 60-89 days (episodic), 90-179 days, 180-364 (long-term), and >365 (persistent). The simulation process to determine the episode length is similar to the simulation process used to determine the predominant drug type in Step 2. After the episode length is determined, another random sampling process is conducted to determine number of days for an episode, which is based on the distribution of the number of days in each episode length category in the MarketScan® data. For example, based on Jane’s profile and her predominant drug of oxycodone, the sampled category of episode length is “30-59 days” and the subsequently sampled number of days is 46 days.

Step 4: Simulate Concurrent Prescription Opioid Use

Concurrent opioid use is defined as receiving two or more different types of prescription opioids from the same pharmacy with an overlapping prescription period. For example, a patient could regularly receive codeine and tramadol from the same pharmacy on the same day, which is considered to be concurrent opioid use.

Predicting concurrent opioid use is also based on a multinomial logistic regression model, with the predictive variables being age, gender, race, predominant drug type and length of episode. Unlike the aforementioned regression models, this one does not rely on predictive values to sample which category the individual is in, because the predicted value is a binomial variable. The likelihood of having concurrent opioid use is as follows

Pconcurrent use=1/(1-exp( 0+ ’age*age_stratum+ ’race*race

+ ’gender*gender+ ’length*length_type+ ’drug*predominant_drug_type))

where is the vector of corresponding coefficient for the vector of covariates. The calculated likelihood is compared with a randomly sampled probability. A likelihood smaller than the randomly generated probability means not having concurrent opioid use in the episode. For example, if Jane’s likelihood is 2.5% and the random generated number is 21.6% (larger than 2.5%), she does not have concurrent opioid use in this episode.

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Step 5: Simulate Overlapping Prescriptions

Overlapping prescriptions are defined as (1) receiving the same type of opioid drug from the same pharmacy with an overlapping prescription period and/or, (2) receiving opioid prescriptions (the same type or not) from multiple pharmacies with an overlapping prescription period. For example, a patient would meet the criteria of having overlapping prescriptions if she receives a 30-day oxycodone prescription from “Pharmacy A” on 6/1/2010 and another 30-day

hydrocodone prescription from “Pharmacy B” on 6/12/2010.

Predicting overlapping prescriptions is based on a multinomial logistic regression model with the same structure as that for concurrent use. The sampling process is also the same. The presence of overlapping prescription and concurrent drug use are assumed to be independent.

Step 6: Simulate Subsequent Episodes of Prescription Opioid Use

The ADOPT model reports all opioid prescriptions that a patient receives during a calendar year (the current version uses 2010). As shown in Figure 3-6, a patient could have multiple episodes of opioid use in 2010. In order to illustrate the prescription history within 2010, the model simulates a 2-year time period from 6/1/2009 to 6/1/2011. The date of the initial episode can begin be any day between 6/1/2009 and 6/1/2010. The length of the gap between two

consecutive episodes is randomly sampled from the distribution of gaps in the MarketScan® data. The model continues to simulate episodes until the end date of the last episode extends beyond 6/1/2011. Only the prescriptions with at least one day’s supply between 1/1/2010 and 12/31/2010 are reported in the model. Eligibility for the PRR program is determined based only on the reported prescriptions. Values reported for cost and efficacy of PRR policy alternatives are for one-year implementation.

Figure 3-6. Subsequent Episodes of Opioid Use

Simulated timespan

Reported timespan

6/1/2009 1/1/2010 12/31/2010 6/1/2011

 Episodes of drug use

To simulate subsequent episodes, the model repeats Steps 2-5. The difference is that one additional variable is added to each regression model –the predicted opioid in the previous episode. For example, if Jane’s previous episode of opioid use is predominantly hydrocodone, she is more likely to use hydrocodone in the subsequent episode. Adding the status of the predicted variable in the previous episode enables the model to account for the association between episodes.

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Step 7: Simulate the Opioid Type of Each Prescription in an Episode

The ADOPT model simulates the opioid type of every prescription in an episode based on the information collected by the model thus far – the predominant opioid drug type, the episode length (number of days), the presence of concurrent drug use, and the presence of overlapping opioid use. For each predominant opioid type and each episode length, ADOPT refers to a specific drug type distribution table. For example, in an episode involving long-acting

oxycodone as the predominant drug type for more than 3 months (i.e. long-term), there is a 7.2%, 4.3%, and 6.8% chance of also having prescriptions for hydrocodone, tramadol, and short-acting oxycodone, respectively (among other unmentioned opioid drugs). The reason for using a specific drug type distribution table is that every predominant opioid has a specific spectrum of associated drugs that are prescribed during the same episode and with specific frequencies. In addition, the spectrum and the frequency distributions of associated drugs are also related to episode length – for example, long-term use of long-acting oxycodone may have a different spectrum and frequency distribution of associated drugs compared to a short-term use of long- acting oxycodone ER.

ADOPT uses a total of 126 opioid type distribution tables (21 predominant opioid types by 6 episode length types). In each distribution table, there are 12 columns, each corresponding to a specific combination of concurrent drug use and overlapping drug use. These 12 columns are organized into four sections (most commonly used, second, third and fourth pharmacy) that present possible overlapping drug use. Each of the four sections contain 3 columns showing different concurrent drug use status including one for no concurrent drug use, one for the primary prescription when concurrent use, and one for companion prescriptions of concurrent use. The primary prescription is defined as follows:

1. the prescribed drug type (could be any opioid type) if only one prescription is in use. Note that in an episode of concurrent drug use, a subject may still have days using only one drug.

2. the predominant drug type if concurrent but different drugs are in use and one of concurrent drugs is predominant

3. either of concurrent drugs if concurrent but different drugs are in use and none of concurrent drugs is predominant. In this case the primary prescription is randomly selected from concurrent drugs.

Companion prescriptions are those not of the primary drug type. For example, if the predominant drug type of Jane’s first episode of opioid use is oxycodone and she has concurrent drug use, then oxycodone is the primary prescription and any concurrent prescription, say hydrocodone, is a companion prescription. If none of two or more concurrent prescriptions is of the predominant drug type, then the order (primary or companion) is randomly assigned.

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Figure 3-7. Example of Opioid Type Distribution Table, for Predominant Drug Type of Hydrocodone and Episode Length between 180- and 364-Days

The most commonly used pharmacy Second pharmacy Third pharmacy Fourth pharmacy

Drug type distributions in second/third/forth pharmacy are used if the subject has overlapping prescriptions Drug type distribution if no concurrent prescription Drug type distribution for primary prescriptions if with concurrent prescription Drug type distribution for companion prescriptions if with concurrent prescription Same structure as in primary pharmacy group Opioid Drug type

If the episode does not have concurrent drug use, then the drug type distribution is based on the column of no concurrent drug use. Otherwise, the drug type distribution is sampled from both the column for primary prescriptions and the column for companion prescriptions.

The four drug type distribution groups for overlapping drug use are prescriptions from the most commonly used, then the second, third, and fourth pharmacies. The most commonly used pharmacy is the one from where the opioid user receives the most prescriptions in a certain period; the second to fourth pharmacies are the places where the user receives numbers of

prescriptions in a descending order. The most commonly used pharmacy does not have to be of a single pharmacy ID in an episode. For example, if Jane receives 3 prescriptions from pharmacy A and 2 from pharmacy B in January, and 2 from pharmacy C and 1 from pharmacy B in February, then the most commonly used pharmacy is A for January and C for February and the second pharmacy is B for both months. In the MarketScan® data we did not observe any users visiting more than 4 pharmacies to obtain overlapping prescriptions. The maximum number of pharmacies in an episode is sampled from the real distribution derived from the MarketScan® data.

Consider Jane’s first episode with the following criteria: 1) Predominant drug type: oxycodone

2) Episode length: 42 days

3) Both concurrent and overlapping drug use (with overlapping prescriptions from a maximum of two pharmacies).

First, the model identifies the drug type distribution table specific to oxycodone and episodic use (30-59 days). Four drug type distribution columns - the second column for primary prescriptions

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and the third column for companion prescriptions in the primary and second pharmacy groups - are used to each sample 40 prescriptions (i.e. 160 prescriptions with assigned drug types in total). The model sampled 40 prescriptions for each prescription type (primary vs. companion) and pharmacy type (primary vs. second vs. third vs. fourth), because no episode in the MarketScan® database exceeded 40 prescriptions in any category of prescription type and pharmacy type in any 2-year period (i.e. the simulated time span). Each 40 prescriptions are stored in a separate area with clear indicators about prescription type and pharmacy type.

Step 8: Simulate the Prescription Details: Generic Name, Strength, Master Form, Quantity, Supply Days, Dose Level and Drug Price

This step involves simulating the details for the list of prescriptions with drug type assigned in the Step 7. The first item to be simulated is the dose level, for two reasons. First, the dose level is key information as it is directly associated with the risk of overdose. Second, the simulated items downstream in the simulation chain are more likely to bear biases because biases may

accumulate during the process. Therefore, the dose level is placed on top of the simulation chain. The second item is supply days. We allow the supply days of an opioid prescription to be any duration between 1-day and 30-days. Prescriptions with supplies exceeding 30-days are very rare (<0.4%) in the MarketScan® data. The distribution of the supply is specific to both dose level and episode length. It is dose-specific because the MarketScan® data show that the supply is

correlated (positively or negatively, depending on drug type) with dose level. For example, a prescription for acute pain may require a prescription with limited days’ supply yet high dosage. It is episode length-specific because a long episode is more likely to be associated with

established, stable prescriptions with greater supply days (e.g. monthly supply).

After the days’ supply is simulated, the model simulates the opioid’s generic name, formulation, and strength in a single step. Each unique combination of generic name, formulation, and

strength for an opioid prescription that appeared in the MarketScan® database is considered as a sub-type of that opioid drug. A dose-level-specific distribution of the subtypes is calculated for each dose level of each drug type. For example, for a daily dose of 187.5mg butalbital and codeine, the chance of having ‘APAP/BUTAL/CAFF/CODEINE’ in a capsule form with strength of “30MG” is 34.2% and the chance of having “ASA/BUTAL/CAFF/ CODEINE” in a capsule form with strength of ‘30MG’ is 65.8%.

The quantity (or the volume, if in solution form) of the prescription opioid is then determined by multiplying the daily dose with the number of supply days, and then divided by the strength. The estimated Medicaid reimbursement for the prescription is calculated by multiplying per unit drug cost (prices per 10 units are listed in Table 3-9) with the quantity. The estimation of per unit costs is detailed in the “Cost Analysis” section of this report.

The simulation of prescription details for each prescription is not always independent. For a long-term episode of opioid use, it is likely that a patient may have an established prescription pattern, meaning a repeated monthly supply of a particular opioid with a stable daily dose. The ADOPT model recognizes an established prescription pattern by allowing any prescription of a predominant drug type with 30-day supply to trigger a stable prescription chain. The prescription chain consists of prescriptions with the same generic name, daily dosage, and days’ supply. The chance of triggering the chain is based on the drug type-, episode length- and dose-specific

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probabilities derived from the MarketScan® data. The number of prescriptions in the chain is sampled from a drug type-, episode length- and dose-specific distribution.

For example, consider Jane’s second episode which lasts 142 days and has hydrocodone as the preliminary drug type. The 6th prescription is “Acetaminophen/ Hydrocodone Bitartrate 325 MG- 10 MG” with 30-day supply and triggers the stable prescription chain. Recall that there is a list of 40 simulated prescriptions with drug types assigned during last step. The next 8 hydrocodone prescriptions are not necessarily the next 8 prescription on the list. For example, they could be